ScienceDirect - Nonlinear Analysis: Real World Applications : Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions

Nonlinear Analysis: Real World Applications
Volume 5, Issue 4, September 2004, Pages 645-665

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doi:10.1016/j.nonrwa.2004.01.004

Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions

E. C. M. Crooks^a, E. N. Dancer^b, D. Hilhorst ^,^,^c, M. Mimura^d and H. Ninomiya^e

^a Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford OX1 3LB, UK ^b School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia ^c Laboratoire de Mathématique, Analyse Numérique et EDP, Université de Paris-Sud, Bat 425, F-91405, Orsay Cedex, France ^d Institute for Nonlinear Sciences and Applied Mathematics, Graduate School of Science, Hiroshima University, 739-8526, Higashi-Hiroshima, Japan ^e Department of Applied Mathematics and Informatics, Ryukoku University, Seta, 520-2194, Otsu, Japan

Received 16 September 2003;

accepted 7 January 2004.

Available online 30 April 2004.

References and further reading may be available for this article. To view references and further reading you must purchase this article.

Abstract

We consider a competition-diffusion system with inhomogeneous Dirichlet boundary conditions for two competitive species and show that they spatially segregate as the interspecific competition rates become large. The limit problem turns out to be a free boundary problem.

Author Keywords: Competition-diffusion system; Singular limit problem; Spatial segregation